Suppose a is n x n matrix and the equation ax = 0 has only the trivial solution. explain why a has n pivot columns and a is row equivalent to in. by theorem 7, this shows that a must be invertible.)
theorem 7: an n x n matrix a is invertible if and only if a is row equivalent to in, and in this case, any sequence of elementary row operations that reduces a to in also transfrms in into a-1.

Remember, a homogeneous system always is consistent. Then we can reason with the rank of the matrix.

If the system Ax=0 has only the trivial solution that's mean that the echelon form of A hasn't free variables, therefore each column of the matrix has a pivot.

Since each column has a pivot then we can form the reduced echelon form of the A, and leave each pivot as 1 and the others components of the column will be zero. This means that the reduced echelon form of A is the identity matrix and so on A is row equivalent to identity matrix.

the answer is thin because within context, the stanza concludes the and frail tone the people have toward each other, and the fact that it would be thin, makes the most sense compared to "pliable" or "not hard or firm to the touch". hope this , good luck.

step-by-step explanation:

can i have brainliest